Vector And Cartesian Equations Of A Line

Step 1: Vector equation of the line.
The vector equation of the line is given by: Where is the position vector of the point , and is the direction vector. Thus, the vector equation of the line is: Which simplifies to:

Step 2: Cartesian equation of the line.
To obtain the cartesian equation, solve for from each of the parametric equations: Equating the values of , we get the cartesian equation:

Final Answer: The vector equation of the line is: The cartesian equation of the line is:

Step 1: Recall the vector equation of a line.
The vector equation of a line passing through a point and parallel to a direction vector is given by:

Step 2: Apply the values.
Here, the position vector , and the direction vector .

Step 3: Write the equation.
The vector equation is:

Step 4: Conclude.
Thus, the correct equation is option (iv).

Final Answer: